Saturday, October 5, 2019

In Search Of Ocean Heat - 8

Follow The Potential Enthalpy
I. Start Here

One of the more oft-written phrases concerning anthropogenic global warming induced climate change is "worse than previously thought."

A long-winded version of that concept has recently made its way into Scientific American magazine (Scientific American, 2019, "Scientists Have Been Underestimating the Pace of Climate Change").

The competent scientists who wrote the article seem to have been intimidated, by the powers that be, into criticizing past in situ gathering methods.

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They exaggerated beyond what they should have:
"The need for revision arises from the long-recognized problem that in the past sea surface temperatures were measured using a variety of error-prone methods such as using open buckets, lamb’s wool–wrapped thermometers, and canvas bags."
(ibid, Scientific American). That is a straw man argument wrapped in irrelevance which will do nothing to improve the analysis of the vast in situ measurement data sets that have for decades been available to researchers who are not lazy.

The "sea surface temperatures" they mentioned are essentially irrelevant in the sense that surface-temperature-only analysis is only a skimming-the-surface type of analysis.

"Real scientists" go deep into the depths of the oceans because real analysis is the deep analysis of those depths rather than merely skimming the surface just to, for example, acquire grant money.

Ignoring highly scientific data from hundreds of years ago (e.g. Newton, 1687 and Woodward, 1888) is a much larger error than "open buckets, lamb’s wool–wrapped thermometers, and canvas bags" used by curious sailors of yesteryear (The World According To Measurements, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20, 21).

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The consequences of ignoring existing data (e.g. World Ocean Database) can not be useful since in situ measurements are observations:
"Because the oceans cover three fifths of the globe, this correction implies that previous estimates of overall global warming have been too low. Moreover it was reported recently that in the one place where it was carefully measured, the underwater melting that is driving disintegration of ice sheets and glaciers is occurring far faster than predicted by theory—as much as two orders of magnitude faster—throwing current model projections of sea level rise further in doubt."
(ibid, Scientific American). The glaciers were known to be melting by scientists working for Oil-Qaeda way back in 1962 when they took out a center-spread advertisement in Life Magazine (Humble Oil-Qaeda), and one of the authors of the Scientific American article "wrote the book" on the impact Humble Oil-Qaeda has had on climate change propaganda (The Exceptional American Denial).

The authors who wrote the Scientific American article, mentioned in Section I above, extol the virtues of temperature as if ocean temperature monitoring is the real problem.

Temperature is not the whole story, as will be shown.

But I agree with them that, for the most part, scientists working in academic endeavors are not as culpable as corporate scientists working under profit motive endeavors are (See e.g. Scientific reticence and sea level rise).

II. How To Use Lotsa Data

I use about 5.5 billion in situ measurements from the WOD 13 database to produce the oceanography oriented posts on Dredd Blog (WOD Update).

Those in situ measurements have to be utilized in a careful process, using the best oceanographic sources (the Thermodynamic Equation Of Seawater - 2010, TEOS-10), and while using the best oceanographic software available (the TEOS-10 toolkit).

Not using a robust data source is one real cause for "worse than previously thought" articles that have been written for years, if not decades.

Yet, the other real cause of the general problem is that some procedures in current software models are not properly constructed:
"In developing the equations for ocean dynamics, it is necessary to
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introduce an equation relating density ρ to pressure P, temperature T, and salinity S ... This relationship is purely empirical, as it arises from the physico-chemical properties of the particular fluid. For seawater ... we also need to write a conservation equation that governs temperature, or, more generally, “heat”. But what is “heat”? It is not temperature, although clearly it is related to temperature. We know that temperature cannot measure heat directly for several reasons, based on measurements of the actual properties of seawater. One is that the temperature increases with pressure. Thus it cannot be a conserved property of an isolated water parcel in the same way that salt content is conserved. We can remove this effect by considering a pressure-corrected variable called potential temperature (about which we shall say more later), but even the potential temperature cannot measure “heat” properly, because the heat capacity of seawater - the amount of energy it takes to change the temperature by 1 K - is not a constant, but varies with temperature and salinity. Thus when mixing parcels of seawater, the temperature of the mixture is not the average of the original temperatures. Instead our understanding of “heat” must be related to energy in some way." - (p.1)

"There is therefore no perfect way to create a conservative heat tracer ... Traditionally, so-called potential temperature has been used as an approximately conservative heat tracer, but doing so cannot be rigorously justified. As we shall show, the best solution currently known is to consider the potential enthalpy ... potential temperature is not conserved under isobaric mixing! Attempting to replace h with θ in eqn. (36) results in all kinds of additional terms on the right hand side of the resulting equation; these result in the “production” of temperature when parcels are mixed. These extra terms have traditionally been ignored, but their effect is in fact noticeable (i.e., lead to predictions that are not matched by observations) when considering ocean processes." (p.11)

"Another variable with the potential property is the potential enthalpy h0 ... Although potential enthalpy is not perfectly conservative ... h0 is effectively conservative. Since the potential enthalpy is a somewhat unusual parameter for oceanographers (and for any- one else!), under TEOS-10 ... a computationally efficient 75-term polynomial is available for this purpose." (pp. 11-12)
(Lecture Overview of Seawater Thermodynamics; accord: Potential Enthalpy: A Conservative Oceanic Variable for Evaluating Heat Content and Heat Fluxes, emphasis added). The TEOS-10 toolkit allows the straightforward calculation of ocean heat (a.k.a. potential enthalpy, h0).

The graphs today show how potential enthalpy is in proportion to Conservative Temperature and thermal expansion and contraction.

The pattern match indicates clearly that thermal expansion and contraction is in a thermodynamic relation with both CT and h0 when the analysis software is configured properly.

The reasons for some of the errors in ocean heat content (OHC) models is not limited to the use of the variable "potential temperature."

The misuse of the mass unit value is also a factor:
"A common practice in sea level research is to analyze separately the variability of the steric and mass components of sea level. However, there are conceptual and practical issues that have sometimes been misinterpreted, leading to erroneous and contradictory conclusions on regional sea level variability. The crucial point to be noted is that the steric component does not account for volume changes but does for volume changes per mass unit (i.e., density changes). This indicates that the steric component only represents actual volume changes when the mass of the considered water body remains constant."
(Journal of Geophysical Research: Oceans, emphasis added). There is a way to derive and use the appropriate mass unit value and keep it fixed while calculating its volume changes over time (thermal expansion and contraction is the changing of volume of a fixed mass unit of seawater over time caused by temperature changes of that fixed mass unit of seawater).

Why is this relevant to the analysis of the impact of global warming induced climate change on the oceans?

It is relevant because without proper search techniques we can't find the OHC we are ostensibly looking for.

III. First Things First

After selecting an array of annual in situ values for temperature (T), salinity (SP), depth ("height" in TEOS-10), latitude, and longitude values in a particular WOD zone, convert them into TEOS-10 values CT (conservative temperature), SA (absolute salinity), and P (pressure).

Thereafter, the first order of business, when properly analyzing TEOS-10 based thermal expansion and thermal contraction, is to calculate the mass unit of seawater being analyzed.

To do that the depth levels must be isolated and their mass unit values determined for each WOD Zone being analyzed.

I calculate the mass unit value of each WOD Zone first, remembering that latitude and longitude boundaries for each such zone vary, because the "l" (length) and "w" (width) in the formula mu = l*w*h varies (not to mention the "h").

In other words, the rectangles may look to be the same size on the WOD map but they actually vary in area and in mass from layer to layer because they are drawn on a globe (spherical trigonometry formulas must be used). [I am working on improved calculations in cases where zones are part ocean and part land near coasts]

For "h" (mass unit height) I use the 33 WOD depth levels enumerated in Appendix 11 of the WOD manual (World Ocean Database User's Manual).

Those 33 depth levels are: 0-10, >10-20, >20-30, >30-50, >50-75, >75-100, >100-125, >125-150, >150-200, >200-250, >250-300, >300-400, >400-500, >500-600, >600-700, >700-800, >800-900, >900-1000, >1000-1100, >1100-1200, >1200-1300, >1300-1400, >1400-1500, >1500-1750, >1750-2000, >2000-2500, >2500-3000, >3000-3500, >3500-4000, >4000-4500, >4500-5000, >5000-5500, >5500 (You can see why I don't use a hand held calculator for this.)

There are other depth levels that could be used, but I use those listed because the WOD manual has valid high and low value ranges for temperature and salinity for each of those depth levels (in all oceans).

I calculate TEOS-10 potential enthalpy values using the toolkit functions:
double s_enthalpy = gsw_enthalpy_ct_exact(SA, CT, P);
double d_enthalpy = gsw_dynamic_enthalpy(SA, CT, P);

h0 = s_enthalpy - d_enthalpy;
Thermal expansion and contraction calculation begins by calculating the Thermal Expansion Coefficient:  tec = gsw_alpha(SA,CT,P).

The thermosteric volume change (thermal expansion or contraction) can then be calculated by:

/*******************************************
  V1 = V0(1 + β ΔT)
  V1 means new thermosteric volume
  V0 means original thermosteric volume
  β means thermal expansion coefficient
  ΔT means change in temperature (tnow - tbefore)
*********************************************/
double StericSLC::thermalExpansion(double mass_unit_vol, /** V0 */
                                                             double tec, /** β */
                                                             double tnow, /** T now */
                                                             double tbefore) /** T before */
{
     double V0 = mass_unit_vol;
     double β = tec;
     double ΔT = tnow - tbefore;
     double V1 = V0 * (1 + (β * ΔT) );

     return V1;
}

(Dredd Blog C++ thermal expansion method).  The V1 value is then divided by 361.841 to derive the sea level change in millimeters (a positive value means thermal expansion, a negative value means thermal contraction).

That exercise must be done for each depth level, then the 33 separate values must be summed to derive the totality of the thermosteric impact on that zone.

The results of the calculations can then be saved into a CSV file to be used for making graphs.

IV. The Graphs

Today's graphs are single zone graphs generated using the process described above.

The thermal expansion and contraction pattern matches the patterns of CT and h0  as one would expect, since they are all thermodynamically proportional to OHC at all depths.

That proportion match means that the thermal expansion and contraction has been calculated correctly.

V. Closing Comments

Ladies and Gentlemen, start your search engines.

This post is a public service of Dredd Blog.

See how hard I work for you?

The previous post in this series is here.

Academy of Sciences member Dr. Eric Rignot: